Runway light Patent

Retractable runway light

The Asymptotics of Wilkinson's Iteration: Loss of Cubic Convergence

One of the most widely used methods for eigenvalue computation is the $QR$ iteration with Wilkinson's shift: here the shift $s$ is the eigenvalue of the bottom $2\times 2$ principal minor closest to the corner entry. It has been a long-standing conjecture that the rate of convergence of the algorithm is cubic. In contrast, we show that there exist matrices for which the rate of convergence is strictly quadratic. More precisely, let $T_X$ be the $3 \times 3$ matrix having only two nonzero entries $(T_X)_{12} = (T_X)_{21} = 1$ and let $T_L$ be the set of real, symmetric tridiagonal matrices with the same spectrum as $T_X$. There exists a neighborhood $U \subset T_L$ of $T_X$ which is invariant under Wilkinson's shift strategy with the following properties. For $T_0 \in U$, the sequence of iterates $(T_k)$ exhibits either strictly quadratic or strictly cubic convergence to zero of the entry $(T_k)_{23}$. In fact, quadratic convergence occurs exactly when $\lim T_k = T_X$. Let $X$ be the union of such quadratically convergent sequences $(T_k)$: the set $X$ has Hausdorff dimension 1 and is a union of disjoint arcs $X^\sigma$ meeting at $T_X$, where $\sigma$ ranges over a Cantor set.Comment: 20 pages, 8 figures. Some passages rewritten for clarit

Lunar surface mechanical properties — Surveyor 1

Engineering telemetry data and lunar surface photographs by Surveyor 1 have been evaluated for information on the mechanical properties of the lunar surface material at the Surveyor 1 landing site. Based primarily on photographic evidence, estimates of soil density, cohesion, and other soil characteristics are presented. Also, the mechanisms in which the lunar material is believed to have failed under the footpad impacts are discussed. Because dynamic soil reactions cannot be interpreted directly from the available data, a comparative study using computer-simulated landings was initiated. Preliminary results of this study, which is still in progress, are presented

Two-sided Grassmann-Rayleigh quotient iteration

The two-sided Rayleigh quotient iteration proposed by Ostrowski computes a pair of corresponding left-right eigenvectors of a matrix $C$. We propose a Grassmannian version of this iteration, i.e., its iterates are pairs of $p$-dimensional subspaces instead of one-dimensional subspaces in the classical case. The new iteration generically converges locally cubically to the pairs of left-right $p$-dimensional invariant subspaces of $C$. Moreover, Grassmannian versions of the Rayleigh quotient iteration are given for the generalized Hermitian eigenproblem, the Hamiltonian eigenproblem and the skew-Hamiltonian eigenproblem.Comment: The text is identical to a manuscript that was submitted for publication on 19 April 200

Lunar surface mechanical properties

The surface material at the Surveyor 5 site is granular and slightly cohesive. Spacecraft footpads plowed trenches in this material as the spacecraft slid during landing. For a compressible soil model, a static bearing capacity of 2.7 newtons/cm^2 gave best agreement with the observations. Static firing of the vernier engines against the surface moved surface particles; a crater 20 cm in diameter and about 1 cm deep was produced, apparently at engine shutdown. The permeability of the soil to gases, to a depth of about 25 cm, is 1 × 10^(−8) cm^2, corresponding to soil particles mostly 2 to 60 μ in diameter

Principal scientific results of the Surveyor 3 Mission

The fine lunar surface material at the Surveyor 3 landing site has about 3 × 10^3-dyne/cm^2 cohesion, 35° angle of internal friction, 3 × 10^5-dyne/cm^2 static bearing capacity. A small rock withstood a local pressure of 2 × 10^7 dynes/cm^2. Soil strength and density increase significantly at depths of a few centimeters. Exposed surface has a considerably higher albedo than the material just below it. The photometric function changed when the surface was slightly compressed. Fine surface material appears to be gradually moving downslope

Principal science results from Surveyor 5

The area of Mare Tranquillitatis in which Surveyor 5 landed appears to be similar to sites in Oceanus Procellarum. The gross elemental composition of the surface material and its response to a magnet are similar to those of a basalt. The debris layer appears to consist of aggregates of the order of 1 cm in diameter consisting of fine grains and set in a matrix of less-coherent fine grains (most of them 2 to 60 μ in diameter) mixed with some rocky fragments 1 mm and larger. The static bearing strength is less than 10^4 dynes/cm^2 for the upper few millimeters and averages approximately 3 × 10^5 dynes/cm^2 for the upper few centimeters. The evidence suggests that chemical differentiation has occurred in the moon, probably owing to internal heat sources; this is consistent with the hypothesis that the maria are basaltic volcanic flows

Rare Copy Number Variants in \u3cem\u3eNRXN1\u3c/em\u3e and \u3cem\u3eCNTN6\u3c/em\u3e Increase Risk for Tourette Syndrome

Tourette syndrome (TS) is a model neuropsychiatric disorder thought to arise from abnormal development and/or maintenance of cortico-striato-thalamo-cortical circuits. TS is highly heritable, but its underlying genetic causes are still elusive, and no genome-wide significant loci have been discovered to date. We analyzed a European ancestry sample of 2,434 TS cases and 4,093 ancestry-matched controls for rare (\u3c 1% frequency) copy-number variants (CNVs) using SNP microarray data. We observed an enrichment of global CNV burden that was prominent for large (\u3e 1 Mb), singleton events (OR = 2.28, 95% CI [1.39–3.79], p = 1.2 × 10−3) and known, pathogenic CNVs (OR = 3.03 [1.85–5.07], p = 1.5 × 10−5). We also identified two individual, genome-wide significant loci, each conferring a substantial increase in TS risk (NRXN1 deletions, OR = 20.3, 95% CI [2.6–156.2]; CNTN6 duplications, OR = 10.1, 95% CI [2.3–45.4]). Approximately 1% of TS cases carry one of these CNVs, indicating that rare structural variation contributes significantly to the genetic architecture of TS

High-Resolution Modeling of the Dust and Water Cycles with the NASA Ames Mars Global Climate Model

NASAs Mars Climate Modeling Center at Ames Research Center is currently undergoing an exciting period of growth in personnel, modeling capabilities, and science productivity. We are transitioning from our legacy Arakawa C-grid finite-difference dynamical core to the NOAA/GFDL cubed-sphere finite-volume dynamical core for simulating the climate of Mars in a global framework. This highly parallelized core is scalable and flexible, which allows for significant improvements in the horizontal and vertical resolutions of our simulations. We have implemented the Ames water ice cloud microphysics package described in Haberle et al. (2018) into this new dynamical core. We will present high-resolution simulations of the dust and water cycles that show that sub-degree horizontal resolution improves the agreement between the vertical distribution of dust and water ice and observations. In particular, both water ice clouds and dust are transported to higher altitudes due to stronger topographic circulations at high resolution. Preliminary results suggest that high-resolution global modeling is needed to properly capture critical features of the dust and water cycles, and thus the current Mars climate